In the Na2SO4-Al2O3 system, the variation in electrical conductivity with composition and dispersoid size stands in stark contrast to that of most other reported composite systems. Two maxima, instead of one, are observed in the conductivity vs, composition plot, at 5.5 and 35 mol% Al2O3. Maximum conductivity enhancement is observed for 35 mol% Al2O3. The increase is about 20 times at 400 degreesC and 450 times at 200 degreesC. Possible conductivity enhancement mechanisms operating in this system are suggested. Surprisingly, the reduction in alumina particle size from 0.5 to 0.004 mum does not bring about any further enhancement in conductivity.